In modern power systems, instability modes have become increasingly diversified following disturbances, necessitating the accurate identification of various instability modes to implement appropriate control measures and prevent significant losses. Therefore, a transient stability assessment method for power systems based on an improved Swin Transformer is proposed in this paper. Firstly, time-domain simulations are conducted to collect voltage magnitude and phase angle characteristics following disturbances, which are used to construct a feature matrix. Then, building upon the Swin Transformer, a spatial cross-scale convolutional attention module is introduced to replace the original multi-head self-attention module. This new module utilizes a series of convolutional layers with different kernel sizes to effectively extract features across multiple dimensions, leading to more accurate prediction results. Finally, simulation experiments on the modified New England 10-machine 39-bus system and IEEE 50 -machine 145-bus system show prediction accuracies of 99.05% and 99.00%, respectively, with multi-swing instability misjudgment rates of 0.35% and 0.27%. These results demonstrate that the proposed method not only accurately predicts different instability modes but also exhibits superior robustness in the presence of noise and missing PMU features.